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LIT-844: Quantum-Like Contextuality in Large Language Models

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Properties6
StatusActive — read in full 2026-10-09 (NOTE-648) from the arXiv preprint (the journal version could not be reached); worth reading as the large-scale test of language-model output for contextuality, and for what its numbers rest on. A PR-prism schema of three sentences ("It is X1 and the same one is X2", "… X2 … same … X3", "… X3 and the other one is X1") is instantiated with 866,108 Simple English Wikipedia noun pairs and their adjectives; BERT gives one referent probability per sentence, and the support is fixed by the schema. Of 51,966,480 models, 77,118 (0.148%) pass the signalling-corrected sheaf test (SF < 1/6) and 36,938,948 (71.1%) the CbD test (Δ < 2). Both verdicts are fixed by three numbers per instance; the CbD one holds whenever BERT is uncertain and roughly consistent across the three sentences. The link to embedding distance is a softmax identity plus weak correlations (R² ≤ 0.08).
Tagscontextuality, linguistics, pragmatics, quantum-foundations, probabilistic-modeling, representation-learning, anthology-candidate
ExtendsLIT-842 — On the Quantum-like Contextuality of Ambiguous Phrases, LIT-016 — The sheaf-theoretic structure of non-locality and contextuality, LIT-265 — The contextual fraction as a measure of contextuality, LIT-831 — Contextuality-by-Default 2.0: Systems with Binary Random Variables
SupportsCLAIM-037 — Formal contextuality is a failure of global extension, distinct from ordinary context dependence, and needs Contextuality-by-Default when marginals shift with context
Cited as “paper” byNOTE-648 — Quantum-Like Contextuality in Large Language Models
Cited as “source” byTHEORY-623 — In the two tests of contextuality in language data that the record has read, the contextuality is put there by the experimenter or not secured: meaning-selection models of ambiguous phrases estimated from corpora are all signalling and their two Contextuality-by-Default verdicts are plausibly noncontextual by their own bootstrap, while BERT's 52 million anaphora models have a support fixed by the sentence schema, so whether each counts as contextual depends only on how uncertain the model's three referent choices are

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Kin Ian Lo, Mehrnoosh Sadrzadeh and Shane Mansfield (2024), Proceedings of the Royal Society A 481(2319): 20240399 (2025), DOI 10.1098/rspa.2024.0399 — ARXIV-2412.16806

Key takeaways

  • The schema fixes the support. “There is an O1 and an O2. (i) It is X1 and the same one is X2. (ii) It is X2 and the same one is X3. (iii) It is X3 and the other one is X1.” The pronouns are the measurements X1–X3 (adjectives), the nouns the outcomes. “Same” puts all mass on the diagonal and “other” on the off-diagonal, so every instance has the support of the PR prism, which is strongly contextual (§5). BERT supplies one number per sentence, P_i(O1), from a masked prediction normalised over the two nouns; the joint distributions are stipulated, not measured.
  • The two tests reduce to three numbers. With ε_i = 2P_i(O1) − 1, the contextual fraction of any such model is 1 and the signalling fraction is max|ε_i| (Propositions 3.3–3.4), so the corrected sheaf criterion CF > 2|M|·SF of Vallée et al. becomes SF < 1/6: every P_i within (5/12, 7/12). The CbD criterion becomes Δ < 2, with Δ = |ε1 − ε2| + |ε2 − ε3| + |ε3 + ε1| (§4).
  • The counts. From 219,633 adjective–noun phrases, 866,108 noun pairs sharing five frequent adjectives give 51,966,480 instances; 77,118 (0.148%) are sheaf-contextual and 36,938,948 (71.1%) CbD-contextual (§6b). Most instances sit at (SF, Δ) = (1, 2), where BERT is certain. Restricted to the top 1% most similar noun pairs, the rates rise to 0.50% and 81.83% (§6c).
  • The geometric “equation”. ε = tanh((p·Δx + Δb)/2) (Proposition 7.1) is the two-way softmax; reading it as proportional to the embedding distance ‖Δx‖ needs isotropic prediction vectors. Euclidean distance is the best of four features, at Pearson 0.08 (full data) and about 0.2 (similar pairs), and cubic R² ≤ 0.009 and 0.08 (Tables 3–6).
  • Inconsistencies in the text. §6c gives the full-data sheaf rate as 0.0148% against 0.148% in §6b and Fig. 5; it cites “Table 2” for the random sample printed as Table 1; Tables 3 and 5 are headed by the two frameworks while the text says they correlate with SF and Δ, so the sign of the correlations cannot be read with certainty.

Standing in the record

Filed on 2026-10-09 at the owner’s direct request, as the BERT study that LIT-842 names among the later work of the Sadrzadeh programme. It is not from the manuscript bibliography: the owner asked for it directly on 2026-10-09. It is the largest claimed case of contextuality in language-related data the record holds, and it is read against THEORY-013 and the claims of line pragmatic-transport in NOTE-648. Its measuring instrument is a language model, not people or a corpus count, and the flag records that its embedding analysis could be held by the anthology.

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